This thesis has two purposes: 1) to document the design of a discrete-time radio receiver for the coherent detection of a QPSK signal in the presence of additive white Gaussian noise; and 2) further research into the performance of representative receivers in the successive demodulation of power-separated, co-channel satellite communications signals. Several commercial companies are offering satellite modulators and demodulators that allow frequency reuse over satellite communications links. There are two methods to demodulate these co-channel signals. The first method requires a priori knowledge of one of the two signals linearly superimposed in the satellite downlink. With this knowledge, the known signal is cancelled using subtraction to reveal the unknown co-channel signal. A second method of recovering both signals is possible if adequate power separation of the two signals allows recovery of the strong signal. After recovery of the strong signal, the data can be re-modulated and then cancelled from the composite signal to reveal the weak signal. This method has the advantage of not requiring a priori information which widens the applications for layered modulation techniques to simplex, broadcast, and multi-cast network architectures.